Question

The LCR circuit becomes extremely sharp in resonance when:

• A. \( R \) is large
• B. \( L \) is large
• C. \( C \) is large
• D. \( R \) is small

Hint:

In an LCR circuit, resonance is sharpest when the resistance is minimal, allowing the current to oscillate with maximum amplitude.

Answer 1

The Correct Option is D

Step 1: Condition for resonance
In a series LCR circuit, resonance occurs when:
\( X_L = X_C \) At this condition, impedance becomes minimum:
\( Z = R \)

Step 2: Sharpness of resonance
The sharpness of resonance is measured by the quality factor:
\( Q = \frac{\omega_0 L}{R} \)

Step 3: Dependence on resistance
From the expression, \(Q\) is inversely proportional to resistance \(R\). Therefore, smaller resistance leads to higher \(Q\) value and sharper resonance.

Final Conclusion:
Thus, resonance is sharpest when resistance \(R\) is small.